On the interpretation of factor analysis

Armstrong, J. Scott and Soelberg, Peer (1968): On the interpretation of factor analysis. Published in: Psychological Bulletin No. 70 (1968): pp. 361-364.

Abstract

The importance of the researcher’s interpretation of factor analysis is illustrated by means of an example. The results from this example appear to be meaningful and easily interpreted. The example omits any measure of reliability or validity. If a measure of reliability had been included, it would have indicated the worthlessness of the results. A survey of 46 recent papers from 6 journals supported the claim that the example is typical, two thirds of the papers provide no measure of reliability. In fact, some papers did not even provide sufficient information to allow for replication. To improve the current situation some measure of factor reliability should accompany applied studies that utilize factor analysis. Three operational approaches are suggested for obtaining measures of factor reliability: use of split samples, Monte Carlo simulation, and a priori models.

• Item Type: MPRA Paper
• Language: English
• Keywords: factor analysis, statistics, marketing
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics; C - Mathematical and Quantitative Methods > C9 - Design of Experiments

References

Burr, C. (1948), “The factorial study of temperamental traits,” British Journal of Psychology, Statistical Section, 1, 178-203.

Cliff, N. & Hamburger, C. D. (1967), “The study of sampling errors in factor analysis by means of artificial experiments,” Psychological Bulletin, 68, 430-445.

Dixon, W. J. (1965), BMD: Biomedical Computer Programs. University of California, Los Angeles, School of Medicine, Department of Preventive Medicine and Public Health.

Guilford, J. P. (1961), “Psychological measurement a hundred and twenty-five years later,” Psychometrika, 26, 101-127.

Guttman, L. (1954), “Some necessary conditions for common-factor analysis,” Psychometrika, 19, 149-161.

Horn, J. L. (1967) “On subjectivity in factor analysis,” Educational and Psychological Measurement, 27, 811-820.

Kaiser, H. F. (1960), “The application of electronic computers to factor analysis,” Educational and Psychological Measurement, 20, 141-151.

Lawlay, D. N. & Maxwell, A. E. (1963), Factor Analysis as a Statistical Method. London: Butterworth.

Rand Corporation (1955), A Million Random Digits with 100,000 Normal Deviates. New York: Free Press.

Solomon, H. (1960), “A survey of mathematical models in factor analysis,” in H. Solomon (Ed.), Mathematical Thinking in the Measurement of Behavior. New York: Free Press.